Furthermore, notice that spacetime structure and causal order as we have defined it are structurally similar: neither one really depends on asymmetry or directedness, and both ultimately instantiate a strict partial order (which is really a bi-order). And indeed, the connection between them has often been recognised. One possible approach to that connection is explored in ref [1]}, which sets up a framework to study the relationship between `causality' in the spacetime structure sense and `causal order' in the process matrix sense. This approach involves embedding a causal structure defined using the process matrix formalism (or another similar information-theoretic formalism) in a spacetime, and then imposing compatibility constraints - for example, a system should only be able to signal to other systems in its future lightcone - so that ordering requirements for processes can be understood as consequences of relativistic causality. An alternative approach is taken by the causal set programme[2]}, which builds spacetime up out of a set of causally related events which are required to stand in a strict partial order. From this point of view, rather than trying to embed a causally ordered structure in a spacetime, we can simply allow the spacetime to emerge from the causally ordered structure. Moreover, the methodology of the process matrix formalism adds a new nuance to this construction, because it allows us to see that the `strict partial order' requirement need not be imposed by fiat but instead could be derived from the need to avoid contradictions (see section REF ), and thus from this point of view, spacetime structure could potentially be regarded as a consequence of basic consistency requirements for valid processes.
